Reversible data hiding (RDH) is an active area of research in the field of information security. For the last few decades variety of approaches were introduced for the purpose of reversible data hiding in digital images. In general, the reversible data hiding techniques can be broadly classified into three categories: histogram shifting based RDH, lossless compression based RDH and difference expansion based RDH. There are many algorithms available in the literature based on the histogram shifting approach. One of the major issues in the histogram shifting based approach is overflow or underflow during the histogram shifting process. In this paper, we propose an efficient technique to handle the overflow or underflow by embedding some additional marking bits in the image during the embedding of the secret message bits. The proposed scheme ensures the exact recovery of the original image and it helps to reduce the overhead of overflow or underflow handling in histogram shifting based RDH scheme. All the experimental study is carried on the standard image data set (USC-SIPI image data set).